Collective magnetic fluctuations in Hubbard plaquettes captured by fluctuating local field method

TL;DR

This paper introduces a Fluctuation Local Field method that improves the modeling of collective magnetic fluctuations in Hubbard systems by incorporating nonlinear fluctuations and local correlations, surpassing traditional mean-field approaches.

Contribution

The paper presents a novel Fluctuation Local Field technique that extends mean-field theories to include nonlinear fluctuations and local correlations in quantum systems.

Findings

Improved magnetic susceptibility calculations for finite Hubbard systems.

Method works effectively at temperatures below the Ne9el temperature.

Provides a broad temperature applicability with manageable computational complexity.

Abstract

We establish a way to handle main collective fluctuations in correlated quantum systems based on a Fluctuation Local Field concept. This technique goes beyond standard mean-field approaches, such as Hartree-Fock and dynamical mean-field theories (DMFT), as it includes a fluctuating classical field that acts on the leading order parameter of the system. Effective model parameters of this new theory are determined from the variational principle, which allows to resolve the Fierz ambiguity in decoupling of the local interaction term. In the saddle-point approximation for the fluctuating field our method reproduces the mean-field result. The exact numerical integration over this field allows to consider nonlinear fluctuations of the global order parameter of the system while local correlations can be accounted by solving the DMFT impurity problem. We apply our method to the magnetic susceptibility of finite Hubbard systems at half-filling and demonstrate that the introduced technique leads to a superior improvement of results with respect to parental mean-field approaches without significant numerical complications. We show that the Fluctuation Local Field method can be used in a very broad range of temperatures substantially below the N\'eel temperature of DMFT, which remains a major challenge for all existing theoretical approaches.